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Fitting an Inhomogeneous Poisson model

1 message · ASANTOS

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ASANTOS
# 
Dear R-Sig-Geo members,

I've like to fitting an Inhomogeneous Poisson model and I have one 
question about better approaches and/or steps order for this.

### Simulating Inhomogeneous Poisson process
library(spatstat)
cI <- rpoispp(function(x, y) {200 * x^2}, lmax = 1000)
cII <- rpoispp(function(x, y) {50 * y^2}, lmax = 1000)
cIII <- rpoispp(function(x,y) {100 * exp(-3*x)}, lmax = 1000)
ant<-superimpose(cI=cI,cII=cII,cIII=cIII)

#Fitting a Poisson model with an intensity that is log-linear in the 
cartesian coordinates with marks
m1<-ppm(ant, ~x + y + marks) # Allows different (constant) intensity for 
each category

#Now I fitting a Inhomogeneous Poisson model with an intensity that is 
log-quadratic in the cartesian coordinates
#with marks

m2<-ppm(ant, ~polynom(x,y,2) + marks)

#Comparing the models
anova(m1,m2,test="Chi")
#Pr(>Chi) = 0.8497 No difference and I choose the more parsimonious 
model m1.

#But if I make the models coefficients inspection:
m1#First model
#????????????? Estimate????? S.E.????? CI95.lo??? CI95.hi Ztest????? Zval
#(Intercept)? 3.0370358 0.3075106? 2.434326133? 3.6397455?? *** 9.876199
#x??????????? 1.3466820 0.3453355? 0.669836907? 2.0235272?? *** 3.899634
#y??????????? 0.6497591 0.3338675 -0.004609147? 1.3041274 1.946159
#markscII??? -1.4190842 0.2877424 -1.983048959 -0.8551194?? *** -4.931787
#markscIII?? -0.6306268 0.2154810 -1.052961828 -0.2082918??? ** -2.926601
m2 #Second model
#?????????????? Estimate????? S.E.?? CI95.lo??? CI95.hi Ztest??????? Zval
#(Intercept)? 3.31439533 0.6095378? 2.119723? 4.5090674?? *** 5.43755529
#x??????????? 0.05883185 1.5736189 -3.025405? 3.1430683 0.03738634
#y??????????? 0.53037435 1.5536416 -2.514707? 3.5754559 0.34137497
#I(x^2)?????? 1.16253158 1.2939978 -1.373658? 3.6987207 0.89840303
#I(x * y)???? 0.04678026 1.1589111 -2.224644? 2.3182043 0.04036570
#I(y^2)?????? 0.08747001 1.2903205 -2.441512? 2.6164518 0.06778937
#markscII??? -1.41908418 0.2877424 -1.983049 -0.8551194?? *** -4.93178655
#markscIII?? -0.63062682 0.2154810 -1.052962 -0.2082918??? ** -2.92660056

I was so astonished with the no significance of I(x^2) by Ztest and my 
question is
whats is the better workflow for improve models of this nature:

1) Try the new models with several cartesian coordinates combinations 
and degrees (first),
2) Try the new models with pair-wise comparison between levels (marks) 
(second),
3) Comparing with null model.

or another approach and/or step order?